855 research outputs found
Structural Relaxation and Frequency Dependent Specific Heat in a Supercooled Liquid
We have studied the relation between the structural relaxation and the
frequency dependent thermal response or the specific heat, , in a
supercooled liquid.
The Mode Coupling Theory (MCT) results are used to obtain
corresponding to different wavevectors. Due to the two-step
relaxation process present in the MCT, an extra peak, in addition to the low
frequency peak, is predicted in specific heat at high frequency.Comment: 14 pages, 13 Figure
Sublinear upper bounds for stochastic programs with recourse
Separable sublinear functions are used to provide upper bounds on the recourse function of a stochastic program. The resulting problem's objective involves the inf-convolution of convex functions. A dual of this problem is formulated to obtain an implementable procedure to calculate the bound. Function evaluations for the resulting convex program only require a small number of single integrations in contrast with previous upper bounds that require a number of function evaluations that grows exponentially in the number of random variables. The sublinear bound can often be used when other suggested upper bounds are intractable. Computational results indicate that the sublinear approximation provides good, efficient bounds on the stochastic program objective value.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47918/1/10107_2005_Article_BF01582286.pd
Inconsistency of the MLE for the joint distribution of interval censored survival times and continuous marks
This paper considers the nonparametric maximum likelihood estimator (MLE) for
the joint distribution function of an interval censored survival time and a
continuous mark variable. We provide a new explicit formula for the MLE in this
problem. We use this formula and the mark specific cumulative hazard function
of Huang and Louis (1998) to obtain the almost sure limit of the MLE. This
result leads to necessary and sufficient conditions for consistency of the MLE
which imply that the MLE is inconsistent in general. We show that the
inconsistency can be repaired by discretizing the marks. Our theoretical
results are supported by simulations.Comment: 27 pages, 4 figure
Observation of Fluctuation-Dissipation-Theorem Violations in a Structural Glass
The fluctuation-dissipation theorem (FDT), connecting dielectric
susceptibility and polarization noise was studied in glycerol below its glass
transition temperature Tg. Weak FDT violations were observed after a quench
from just above to just below Tg, for frequencies above the alpha peak.
Violations persisted up to 10^5 times the thermal equilibration time of the
configurational degrees of freedom under study, but comparable to the average
relaxation time of the material. These results suggest that excess energy flows
from slower to faster relaxing modes.Comment: Improved discussion; final version to appear in Phys. Rev. Lett. 4
pages, 5 PS figures, RevTe
Excited states of linear polyenes
We present density matrix renormalisation group calculations of the Pariser-
Parr-Pople-Peierls model of linear polyenes within the adiabatic approximation.
We calculate the vertical and relaxed transition energies, and relaxed
geometries for various excitations on long chains. The triplet (3Bu+) and even-
parity singlet (2Ag+) states have a 2-soliton and 4-soliton form, respectively,
both with large relaxation energies. The dipole-allowed (1Bu-) state forms an
exciton-polaron and has a very small relaxation energy. The relaxed energy of
the 2Ag+ state lies below that of the 1Bu- state. We observe an attraction
between the soliton-antisoliton pairs in the 2Ag+ state. The calculated
excitation energies agree well with the observed values for polyene oligomers;
the agreement with polyacetylene thin films is less good, and we comment on the
possible sources of the discrepencies. The photoinduced absorption is
interpreted. The spin-spin correlation function shows that the unpaired spins
coincide with the geometrical soliton positions. We study the roles of
electron-electron interactions and electron-lattice coupling in determining the
excitation energies and soliton structures. The electronic interactions play
the key role in determining the ground state dimerisation and the excited state
transition energies.Comment: LaTeX, 15 pages, 9 figure
Random Matrix Theory of Transition Strengths and Universal Magnetoconductance in the Strongly Localized Regime
Random matrix theory of the transition strengths is applied to transport in
the strongly localized regime. The crossover distribution function between the
different ensembles is derived and used to predict quantitatively the {\sl
universal} magnetoconductance curves in the absence and in the presence of
spin-orbit scattering. These predictions are confirmed numerically.Comment: 15 pages and two figures in postscript, revte
Dielectric and thermal relaxation in the energy landscape
We derive an energy landscape interpretation of dielectric relaxation times
in undercooled liquids, comparing it to the traditional Debye and
Gemant-DiMarzio-Bishop pictures. The interaction between different local
structural rearrangements in the energy landscape explains qualitatively the
recently observed splitting of the flow process into an initial and a final
stage. The initial mechanical relaxation stage is attributed to hopping
processes, the final thermal or structural relaxation stage to the decay of the
local double-well potentials. The energy landscape concept provides an
explanation for the equality of thermal and dielectric relaxation times. The
equality itself is once more demonstrated on the basis of literature data for
salol.Comment: 7 pages, 3 figures, 41 references, Workshop Disordered Systems,
Molveno 2006, submitted to Philosophical Magazin
Acoustic and relaxation processes in supercooled o-ter-phenyl by optical-heterodyne transient grating experiment
The dynamics of the fragile glass-forming o-ter-phenyl is investigated by
time-resolved transient grating experiment with an heterodyne detection
technique in a wide temperature range. We investigated the dynamics processes
of this glass-former over more then 6 decades in time with an excellent
signal/noise. Acoustic, structural and thermal relaxations have been clearly
identify and measured in a time-frequency window not covered by previous
spectroscopic investigations. A detailed comparison with the density response
function, calculated on the basis of generalized hydrodynamics model, has been
worked out
Frequency dependent specific heat of viscous silica
We apply the Mori-Zwanzig projection operator formalism to obtain an
expression for the frequency dependent specific heat c(z) of a liquid. By using
an exact transformation formula due to Lebowitz et al., we derive a relation
between c(z) and K(t), the autocorrelation function of temperature fluctuations
in the microcanonical ensemble. This connection thus allows to determine c(z)
from computer simulations in equilibrium, i.e. without an external
perturbation. By considering the generalization of K(t) to finite wave-vectors,
we derive an expression to determine the thermal conductivity \lambda from such
simulations. We present the results of extensive computer simulations in which
we use the derived relations to determine c(z) over eight decades in frequency,
as well as \lambda. The system investigated is a simple but realistic model for
amorphous silica. We find that at high frequencies the real part of c(z) has
the value of an ideal gas. c'(\omega) increases quickly at those frequencies
which correspond to the vibrational excitations of the system. At low
temperatures c'(\omega) shows a second step. The frequency at which this step
is observed is comparable to the one at which the \alpha-relaxation peak is
observed in the intermediate scattering function. Also the temperature
dependence of the location of this second step is the same as the one of the
peak, thus showing that these quantities are intimately connected to
each other. From c'(\omega) we estimate the temperature dependence of the
vibrational and configurational part of the specific heat. We find that the
static value of c(z) as well as \lambda are in good agreement with experimental
data.Comment: 27 pages of Latex, 8 figure
Models and model value in stochastic programming
Finding optimal decisions often involves the consideration of certain random or unknown parameters. A standard approach is to replace the random parameters by the expectations and to solve a deterministic mathematical program. A second approach is to consider possible future scenarios and the decision that would be best under each of these scenarios. The question then becomes how to choose among these alternatives. Both approaches may produce solutions that are far from optimal in the stochastic programming model that explicitly includes the random parameters. In this paper, we illustrate this advantage of a stochastic program model through two examples that are representative of the range of problems considered in stochastic programming. The paper focuses on the relative value of the stochastic program solution over a deterministic problem solution.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44253/1/10479_2005_Article_BF02031741.pd
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